Simulating the electrophysiology of discretely-coupled cardiac cells - PowerPoint PPT Presentation

Simulating the electrophysiology of discretely-coupled cardiac cells in a multi-domain formulation C. Houston, E. Dupont, R.A. Chowdhury, N.S. Peters, S.J. Sherwin, C.D. Cantwell ElectroCardioMaths Programme, Imperial College London Nektar++ Workshop, 11 June 2019

Outline • Introduction to cardiac electrophysiology • Discrete-cell model in Nektar++ • Initial validation results • Conclusions & Future work

Outline • Introduction to cardiac electrophysiology • Introduction to cardiac electrophysiology • Discrete-cell model in Nektar++ • Initial validation results • Conclusions & Future work

What’s in a heartbeat? JHeuser, 2005. AC Guyton and JE Hall. Textbook of Medical Physiology. 1996. S Rohr. Role of gap junctions in the propagation of cardiac action potential. Cardiovasc Res. 2004. N Sperelakis, K McConnell. Electric field interactions between closely abutting excitable cells. IEEE engineering in medicine and biology magazine . 2002 Jan;21(1):77-89.

What’s in a heartbeat? JHeuser, 2005. Adapted from Guyton and Hall, 1996. Fig 9-2. AC Guyton and JE Hall. Textbook of Medical Physiology. 1996. S Rohr. Role of gap junctions in the propagation of cardiac action potential. Cardiovasc Res. 2004. N Sperelakis, K McConnell. Electric field interactions between closely abutting excitable cells. IEEE engineering in medicine and biology magazine . 2002 Jan;21(1):77-89.

What’s in a heartbeat? Rohr, 2004. Fig 3. JHeuser, 2005. Adapted from Guyton and Hall, 1996. Fig 9-2. Sperelakis, 2002.. AC Guyton and JE Hall. Textbook of Medical Physiology. 1996. S Rohr. Role of gap junctions in the propagation of cardiac action potential. Cardiovasc Res. 2004. N Sperelakis, K McConnell. Electric field interactions between closely abutting excitable cells. IEEE engineering in medicine and biology magazine . 2002 Jan;21(1):77-89.

Modelling cardiac electrophysiology Pathmanathan et al, 2018. P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology Pathmanathan et al, 2018. P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology Cantwell et al, 2015. Pathmanathan et al, 2018. P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology Cantwell et al, 2015. Pathmanathan et al, 2018. • Steep spatial gradient at wavefront. • Sti ff ness of ODE cell model. • Geometric complexity. P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Organ-scale rotational activity Cantwell CD et al. High-order spectral/hp element discretisation for reaction–di ff usion problems on surfaces: Application to cardiac electrophysiology. Journal of computational physics. 2014 Jan 15;257:813-29.

Biological preparation Houston C et al. Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line. Journal of molecular and cellular cardiology. 2018 Jun 1;119:155-64.

Cell-scale rotational activity Houston C et al. Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line. Journal of molecular and cellular cardiology. 2018 Jun 1;119:155-64.

Hypothesis & Aims We hypothesise that conduction features at a cellular level are a key factor in the initiation and perpetuation of re-entrant arrhythmias and fibrillation in vivo . We aim to develop the first biophysically-validated and morphologically-accurate discrete cell model for action potential propagation in cardiac cell monolayers.

Outline • Introduction to cardiac electrophysiology • Introduction to cardiac electrophysiology • Discrete-cell model in Nektar++ • Discrete-cell model in Nektar++ • Initial validation results • Conclusions & Future work

Idealised model for cable of cells M M GJ G cell i+1 ... ... cell i

Idealised model for cable of cells M M GJ G cell i+1 ... ... cell i

Idealised model for cable of cells M M GJ G cell i+1 ... ... cell i

Idealised model for cable of cells M M GJ G cell i+1 ... ... cell i ( L + Λ ) û = f L = discrete Laplacian Λ = interface coupling

Multi-domain global matrix system Interfaces Extracellular space Cells L

Multi-domain global matrix system Interfaces Extracellular space Cells L + Λ

Outline • Introduction to cardiac electrophysiology • Discrete-cell model in Nektar++ • Initial validation results • Conclusions & Future work

Steady-state solution for fixed potential at cable end λ g =0.11cm λ g =0.09cm λ g =0.07cm 0 0 0 Voltage (AU) -0.1 .1 .1 -0.2 .2 .2 Intracellular Intracellular Intracellular Extracellular Extracellular Extracellular Transm em brane Transm em brane Transm em brane -0.3 .3 .3 0 0.05 0.1 0.15 0 0.05 0.1 0.15 0 0.05 0.1 0.15 Length (cm ) Length (cm ) Length (cm ) Increased gap junction resistance leads to greater λ g R g proportion of decay across gap junctions.

Steady-state solution for current injected into cable λ g =0.11cm λ g =0.09cm λ g =0.07cm 0.1 0.1 0.1 Transm em brane voltage (AU) 0.05 05 05 0 0 0 Analytic Analytic Analytic -0.05 05 05 Sim ulation Sim ulation Sim ulation -0.1 .1 .1 0 0.05 0.1 0.15 0 0.05 0.1 0.15 0 0.05 0.1 0.15 Length (cm ) Length (cm ) Length (cm ) ‘Speed bumps’ at gap junctions as current λ g R g redistributes for path of least resistance.

Outline • Introduction to cardiac electrophysiology • Discrete-cell model in Nektar++ • Initial validation results • Conclusions & Future work

Conclusions We have constructed a multi-domain formulation within the Nektar++ framework to solve steady-state solutions for cell- level conduction in cardiac electrophysiology. The framework reproduces known analytical solutions for a cable of connected cardiac cells.

What’s next? Incorporate time-dependent features at interfaces (i.e. cell model ODEs). Direct biophysical validation of our model with one-to-one matching biological preparations. Prediction of e ff ects of changes to intercellular coupling on cell-scale conduction patterns. • Generalise multi-domain support in the library. • Parallelise solving in separate domains.

Acknowledgements Supervisors Dr Chris Cantwell Dr Rasheda A Chowdhury Prof Spencer Sherwin Prof Nicholas S Peters Dr Emmanuel Dupont (past) ElectroCardioMaths Group Dr David Pitcher Dr Fu Siong Ng PhD Assessors Prof Denis Doorly Prof Cesare Terraciano

1D steady-state solutions A B C 0 Voltage (AU) -0.1 -0.2 Intracellular potential Extracellular potential -0.3 Transm em brane potential 0 0.05 0.1 0.15 0 0.05 0.1 0.15 0 0.05 0.1 0.15 Length (cm) Length (cm) Length (cm) A B 1 0.1 Transmembrane potential, AU Transmembrane potential, AU 0.5 0.05 0 0 -0.5 -0.05 Analytical Simulation -1 -0.1 0 0.2 0.4 0.6 0.8 1 0.56 0.58 0.6 0.62 0.64 Length, cm Length, cm

Idealised model for cable of cells M M GJ G cell i+1 ... ... cell i ( L + Λ ) û = f L = discrete Laplacian Λ = interface coupling

Conduction block/slowing algorithm C Houston et al. Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line. J Mol Cell Cardio . 2018. B Handa et al. Analytical approaches for myocardial fibrillation signals. Comput. Biol. Med. 2018.